The calls are understood to have the support of the Labour deputy leader Harriet Harman, as well as figures in the Labour whip's office.
Facing huge financial pressures, Labour is angry at the prospect of having to fight a string of expensive byelections in safe Labour seats that would drain party resources away from targeting marginal seats later in this parliament, or at the next election.
Labour officials say no decision has been made on whether to ask the national executive formally to review the position.
It would be possible in the case of a mayoral election to tell a sitting Labour MP that if they resign as an MP they will be prevented from seeking the Labour nomination to be mayor.
Labour is not due to start the process of selecting its mayoral candidates until after the referendums on 3 May.
But both Liam Byrne, the shadow work and pensions secretary and MP for Birmingham Hodge Hill, and Gisela Stuart, the Labour MP for Birmingham Edgbaston, have said they will seek the nomination to be Birmingham's first elected mayor. A third candidate, Sion Simon, stood down as a Labour MP at the last election, and he would greatly benefit if Byrne and Stuart could not seek the Labour nomination.
Labour's ruling national executive committee (NEC) will hold an interview panel in the middle of May to select mayoral candidates, and ballot papers for electing Labour's mayoral nominees are due to go out on 25 May.
Stuart, an acknowledged campaigner, held her seat with a majority of just 1,274, keeping the swing to the Tories down below 2%. Byrne held his seat with a comfortable 10,302 majority, and now claims the support of the Labour leader on Birmingham council, Sir Albert Bore.
It would be a big and politically controversial step to prevent the two MPs from seeking the mayoralty of England's second city.
In the case of Stuart, she has been clear she was campaigning for the Labour nomination for months.
There was no comment from Harman's office on Monday night.
But one source said: "This is a live issue of concern. Byelections are very expensive and, as Bradford showed, unpredictable. There is a lot of evidence that voters do not like being asked to come out and vote time and again. You cannot prevent an MP from resigning, but it is open to the party to say to an MP you cannot seek the Labour nomination to be mayor."
Eleven cities are holding referendums in May on whether to have a directly elected mayor. If a city votes yes, then the elections will be held in November on the same date as the elections for the 41 new police commissioners.
It is not expected that more than four cities at the outside will vote yes for a mayor, but the outcomes are highly unpredictable. In some cities, such as Leeds, all party campaigns have been formed to prevent any change to the current system of local government.
Labour is more advanced in selecting its police commissioner candidates, and in the case of Greater Manchester, Tony Lloyd, the MP for Manchester Central, has already been approved by a national executive panel as the only Labour candidate for what is expected to be a £100,000-a-year job.
He has also stood down as chairman of the parliamentary Labour party. A byelection for his seat would be held on 15 November, the same date as the police commissioner elections in England and Wales.
Alun Michael, former home office minister under Tony Blair, is hoping to become police commissioner for South Wales. He held his parliamentary seat in the 2010 election with a majority of 4,709.
